fr_count_x=c(0,1,2,6,7,9,10,11,13,24,26,27,28,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,288,289,290,291,292,293,295,296,297,298,299,301,302,303,304,305,307,308,310,311,312,313,314,316,317,318,319,321,323,324,325,326,327,328,329,330,331,332,333,334,336,338,340,343,344,349,351,352,356,360,366,367,371,374,375,378,380,384,385,394,396,402,409,412,420,422,437,446,468,474,481,496,503,512,520,521,523,531,532,560,568,573,586,592,604,607,619,626,627,630,671,672,677,694,704,706,707,715,745,773,781,807,827,854,876,927,946,964,976,982,1021,1031,1039,1047,1049,1056,1085,1145,1148,1152,1155,1159,1168,1178,1180,1191,1295,1349,1367,1368,1408,1413,1416,1451,1468,1474,1532,1557,1570,1593,1636,1690,1733,1755,1818,1823,1864,1889,1947,1983,2010,2019,2107,2114,2124,2155,2174,2193,2195,2197,2218,2232,2252,2300,2354,2424,2432,2445,2507,2571,2573,2618,2631,2715,2836,2847,2878,2915,2973,3014,3034,3053,3068,3096,3153,3197,3201,3209,3287,3319,3358,3363,3424,3441,3458,3459,3482,3489,3499,3569,3574,3593,3628,3634,3635,3745,3771,3774,3781,3789,3958,4064,4072,4083,4089,4094,4242,4250,4329,4355,4361,4394,4710,4725,4754,4772,4797,4804,4880,4882,4886,4916,4939,4976,4996,5020,5130,5159,5169,5174,5349,5413,5439,5535,5556,5588,5612,5695,5739,5868,5901,5941,5954,5976,6050,6064,6067,6100,6119,6177,6195,6198,6216,6331,6347,6453,6454,6486,6529,6556,6558,6592,6630,6658,6688,6695,6708,6804,6877,6924,6930,6960,7018,7049,7149,7216,7244,7259,7307,7444,7504,7507,7557,7564,7585,7588,7595,7597,7613,7659,7710,7719,7786,7867,7977,7983,7997,8019,8119,8164,8212,8242,8250,8281,8403,8425,8430,8446,8496,8617,8651,8657,8715,8740,8799,8807,8826,8875,8948,8953,8976,8983,8992,9014,9016,9088,9248,9250,9288,9290,9417,9510,9566,9584,9649,9667,9798,9807,9808,9853,9977,9987,9996,9998,10004,10015,10115,10135,10136,10155,10192,10196,10198,10227,10243,10247,10260,10416,10568,10602,10609,10641,10724,10771,10861,10957,11202,11205,11213,11240,11241,11244,11265,11267,11321,11402,11409,11432,11444,11445,11492,11545,11565,11701,11831,11903,11986,12062,12067,12085,12123,12196,12224,12225,12263,12297,12371,12396,12399,12402,12451,12503,12544,12571,12674,12685,12701,12733,12792,12826,12856,12996,12997,13011,13041,13047,13110,13170,13183,13341,13474,13476,13583,13627,13678,13732,13775,13797,13801,13806,13955,14105,14134,14138,14265,14301,14305,14474,14524,14573,14595,14621,14694,14714,14750,14761,14919,14947,14955,15003,15015,15082,15107,15108,15153,15224,15246,15339,15347,15512,15555,15646,15694,15698,15718,15734,15832,15889,16006,16030,16170,16204,16212,16460,16600,16701,16714,16755,16824,16959,16965,17016,17025,17026,17098,17153,17233,17239,17377,17425,17429,17489,17491,17509,17539,17576,17589,17738,17814,17850,17872,17896,17916,17932,17987,18048,18064,18190,18192,18231,18255,18311,18441,18526,18626,18693,18791,18805,18809,18830,18943,18990,19061,19117,19172,19177,19257,19312,19410,19474,19499,19519,19529,19621,19683,19740,19804,19814,19854,19891,19908,20016,20135,20231,20249,20382,20685,20833,20846,20887,20964,21084,21138,21159,21163,21196,21246,21255,21356,21391,21408,21530,21609,21668,21760,21769,21825,21960,21970,22128,22140,22172,22197,22198,22221,22268,22310,22312,22314,22368,22375,22384,22400,22411,22483,22538,22680,22698,22719,22759,22761,22826,22828,22975,23165,23175,23196,23363,23365,23426,23438,23527,23610,23613,23639,23649,23917,23922,24192,24208,24233,24280,24326,24327,24357,24359,24372,24421,24428,24451,24453,24504,24512,24524,24526,24528,24537,24598,24618,24634,24676,24679,24763,24807,24836,24844,24871,24886,24947,24951,25003,25031,25051,25110,25120,25133,25208,25213,25265,25279,25373,25377,25381,25387,25403,25452,25485,25487,25504,25515,25570,25601,25608,25642,25707,25711,25800,25806,25810,25866,25889,25909,25921,25948,25959,25983,25984,26000,26001,26012,26063,26074,26103,26111,26166,26221,26244,26281,26300,26308,26309,26332,26334,26337,26347,26357,26379,26390,26392,26404,26409,26412,26429,26434,26437,26440,26459,26476,26487,26503,26516,26582,26615,26628,26646,26679,26685,26696,26706,26743,26748,26749,26751,26753,26762,26798,26802,26805,26842,26854,26877,26882,26887,26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fr_count_y=c(0,1,2,1,1,3,1,1,1,1,2,1,1,3,1,1,1,3,4,4,6,4,11,5,5,10,9,7,7,4,7,12,18,19,14,15,18,16,39,25,30,24,38,33,44,41,32,43,43,62,50,53,70,88,71,92,99,95,120,122,145,146,151,169,178,215,209,222,210,260,264,259,279,298,363,399,476,459,451,479,577,574,550,589,645,628,672,732,743,741,771,818,740,740,802,826,869,801,846,786,885,817,783,869,823,820,814,802,805,716,776,752,760,774,676,684,642,676,646,597,641,564,586,516,515,498,501,501,476,477,450,464,445,459,436,419,379,383,351,355,347,293,348,341,339,321,279,317,264,277,292,288,267,253,241,252,257,238,240,246,238,210,208,207,182,198,192,212,171,183,176,167,162,163,166,150,156,179,143,152,131,133,113,138,121,126,110,138,109,115,93,104,123,88,92,74,95,94,73,86,73,63,50,65,66,71,61,60,47,64,52,51,46,52,51,55,31,33,40,42,43,28,34,33,32,48,31,32,24,36,28,32,36,32,25,25,35,32,36,33,30,25,30,28,19,20,16,36,17,26,25,14,19,15,14,16,11,12,7,13,12,13,8,6,7,6,7,8,5,1,1,2,2,3,1,1,3,2,5,2,1,1,4,2,1,1,2,1,1,4,4,2,2,1,2,2,1,1,1,1,1,3,1,2,3,2,4,3,1,1,2,1,1,1,1,4,1,2,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,2,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,5,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,1,1,1,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,2,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,3,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,3,1,2,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,3,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,3,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,2,1,1,4,1,1,1,1,1,1,1,1,1,1,1,3,2,1,1,3,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,3,2,1,1,1,1,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,3,1,2,1,2,1,1,1,2,2,1,2,1,1,2,1,1,1,1,1,3,1,7,1,2,1,2,1,2,1,7,1,3,1,1,3,4,1,1,1,1,9,1,1,2,1,2,1,1,1,8,1,1,1,2,2,1,1,1,1,1,2,1,3,1,1,2,1,2,1,3,1,4,1,1,1,1,1,2,1,2,3,8,1,2,1,1,1,1,1,1,2,1,3,1,2,2,1,2,1,3,3,2,1,1,1,1,1,1,1,2,3,1,1,5,1,1,1,2,1,1,1,2,1,2,1,1,1,1,1,1,1,1,1,1,2,4,2,1,1,2,3,3,1,2,1,1,2,1,6,1,1,1,1,1,1,5,1,1,3,1,1,1,1,1,1,1,6,1,3,1,1,2,2,1,3,2,1,1,1,1,1,1,2,1,1,1,6,1,1,1,1,2,1,2,1,3,1,1,1,1,3,2,1,1,1,1,1,2,1,1,2,1,1,1,1,1,1,1,2,2,1,1,1,1,2,1,2,1,3,1,1,1,2,2,1,1,1,1,1,1,1,1,2,1,2,1,1,1,2,3,2,1,1,2,1,1,1,2,2,1,1,1,2,1,1,2,1,1,1,1,1,1,1,1,3,1,1,1,1,1,3,1,1,1,1,1,1,3,1,1,3,1,1,7,2,2,1,1,1,8,1,1,1,1,1,1,1,2,3,2,2,1,1,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,4,2,1,1,2,1,1,1,3,1,2,1,1,1,1,1,2,1,3,1,1,2,1,1,2,1,1,1,2,1,5,1,1,2,3,3,2,5,1,1,2,2,4,1,2,1,2,2,1,1,11,1,2,1,1,2,3,1,3,1,2,1,1,1,7,1,2,1,1,1,3,2,2,4,1,1,1,2,1,2,1,1,1,1,2,1,1,1,1,1,3,2,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,5,1,2,1,1,2,1,1,1,1,4,1,3,1,6,1,4,1,2,1,1,1,5,1,1,1,2,1,1,1,1,1,2,1,1,2,8,1,1,1,4,4,1,3,4,2,2,1,2,3,1,1,1,1,2,1,1,1,1,2,1,1,1,2,3,1,1,2,3,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,2,3,2,2,3,4,1,1,1,1,1,5,3,3,9,1,1,3,2,3,1,1,1,1,1,1,1,2,2,1,4,1,1,3,1,4,1,1,1,2,1,2,1,1,1,2,4,2,1,2,1,1,4,1,3,2,2,2,2,1,1,1,1,3,2,3,3,3,1,5,5,6,1,1,3,4,3,1,1,2,1,1,2,3,1,1,5,1,1,1,4,1,2,2,2,1,1,4,1,3,1,2,2,1,1,2,2,1,4,2,3,1,1,4,5,6,6,2,8,1,2,2,2,1,1,3,3,2,2,2,2,1,1,1,3,2,2,2,3,2,1,1,1,1,1,1,4,1,4,1,2,1,2,1,3,1,1,1,2,1,1,2,1,1,3,1,1,2,1,1,3,2,6,1,2,2,1,1,1,1,2,1,1,1,1,2,1,1,1,1,1,3,2,1,1,2,1,1,1,7,13,2,2,1,1,2,3,1,1,3,4,1,1,1,1,2,1,1,1,1,3,1,1,1,1,3,3,1,3,2,2,1,1,3,1,2,1,2,1,1,1,1,1,1,2,2,2,1,2,3,1,2,1,1,4,1,1,1,5,3,5,1,3,1,2,2,1,1,1,3,2,2,1,1,1,2,1,2,4,1,3,2,1,1,1,2,1,2,2,3,5,2,1,1,1,2,2,1,4,1,1,1,1,1,2,2,8,3,4,2,1,1,2,2,2,1,2,1,5,2,1,4,2,1,1,2,3,1,2,2,2,14,2,2,1,1,1,1,1,1,2,1,1,2,3,1,9,2,1,1,2,2,2,1,2,1,2,2,1,2,1,2,1,2,3,2,1,3,4,3,3,1,1,2,6,5,1,1,1,5,3,2,1,1,1,1,1,1,2,3,6,6,1,1,1,6,1,4,2,2,2,4,2,2,1,1,2,1,1,2,1,1,2,4,2,1,1,1,3,2,2,1,2,1,2,1,1,4,2,1,4,1,5,3,1,1,1,2,5,5,1,1,3,1,1,1,2,2,3,2,2,1,1,1,1,4,1,2,1,1,1,1,2,2,1,2,2,5,2,1,3,2,1,1,1,2,2,2,4,2,8,1,2,1,7,10,2,3,2,1,3,1,6,5,4,2,1,1,2,1,2,1,1,2,1,1,3,1,1,1,6,7,1,1,3,2,2,1,3,2,3,1,2,4,1,5,2,1,1,7,5,2,2,2,1,1,1,2,1,1,1,1,1,2,1,1,1,2,3,2,6,3,2,1,1,2,2,2,1,2,2,1,1,1,2,1,2,1,5,3,1,3,2,17,1,2,2,1,1,1,2,2,8,1,5,1,7,4,2,1,5,1,6,2,1,1,3,1,1,1,2,3,5,7,1,2,3,2,2,1,5,1,1,3,1,3,1,4,1,2,3,3,1,1,1,1,1,3,1,2,7,2,2,3,2,6,6,2,1,3,2,2,3,2,2,1,1,2,2,1,4,2,2,7,2,2,2,1,2,1,1,1,1,1,3,5,1,3,4,1,5,1,2,4,2,1,2,2,5,3,1,3,1,2,1,2,2,3,1,1,3,1,5,4,1,3,2,9,3,1,2,1,1,5,1,2,1,2,2,3,3,3,3,1,1,2,1,3,1,4,1,1,5,5,5,1,1,1,3,6,7,1,1,5,4,1,3,20,2,1,3,3,9,2,3,6,5,2,6,1,2,2,1,1,2,3,2,6,4,2,3,6,3,2,4,2,1,3,1,4,1,1,1,1,2,2,1,2,4,5,1,1,2,1,2,3,4,1,1,1,4,4,2,5,1,3,2,4,2,1,1,1,5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5,2,1,13,6,4,3,8,8,6,4,9,8,2,9,8,16,10,5,11,14,16,3,3,4,6,10,7,7,8,9,3,3,4,3,7,8,10,8,9,8,4,3,4,12,5,2,11,4,9,8,3,4,11,4,4,4,3,4,3,3,6,8,2,6,5,4,17,5,3,1,2,3,7,1,6,7,5,9,5,16,1,5,5,8,5,2,9,1,5,6,9,5,8,7,10,6,15,10,4,12,3,6,8,12,6,5,8,9,9,3,14,7,11,2,8,4,7,6,3,9,3,7,1,12,4,7,6,4,8,5,7,6,4,9,8,2,5,3,12,12,7,2,17,13,2,11,5,5,7,8,9,7,7,9,4,4,18,4,15,13,8,2,3,22,13,6,5,7,2,12,3,9,4,6,6,3,5,2,9,4,8,7,1,9,13,8,8,12,17,6,2,9,6,5,4,3,7,9,17,6,7,3,4,3,7,8,3,10,6,4,9,15,7,9,7,3,7,10,5,7,9,8,2,2,5,17,5,2,3,3,7,5,11,9,8,8,15,8,10,8,4,5,6,13,8,12,5,6,12,2,7,11,3,7,7,7,19,5,10,2,9,17,1,8,6,7,6,4,24,6,6,7,4,6,6,1,4,4,14,14,1,3,14,7,10,4,4,6,2,4,9,7,17,8,2,2,9,26,14,6,5,7,6,4,4,3,4,4,7,6,7,7,7,7,5,4,7,8,1,7,8,9,4,3,7,10,5,8,8,9,4,15,8,5,5,3,9,3,2,6,5,13,4,4,3,18,8,9,12,14,13,10,4,4,6,10,7,9,11,6,6,10,11,11,6,7,5,6,13,14,7,15,4,10,6,8,3,5,6,4,7,4,11,10,8,10,9,6,6,15,14,9,4,6,2,7,6,5,8,3,4,5,12,4,1,5,5,11,7,11,3,7,5,7,4,6,6,2,4,2,1,13,3,11,4,6,2,2,2,10,5,6,7,11,6,2,6,9,6,7,7,3,2,4,6,14,8,16,12,10,8,3,7,9,6,3,13,6,3,2,2,6,8,1,1,8,6,7,11,2,9,10,6,4,1,5,3,5,14,5,4,1,7,14,3,13,5,11,8,5,5,8,3,6,6,9,11,6,7,6,1,6,4,6,3,5,3,7,7,6,7,4,12,5,1,5,3,1,7,4,4,6,3,10,4,6,4,10,8,5,10,10,12,6,6,6,3,4,14,9,10,5,4,8,10,10,11,12,12,6,3,9,6,3,3,7,2,7,6,7,15,6,3,9,2,2,7,9,7,3,8,11,9,5,4,7,6,16,3,4,9,8,2,4,12,4,12,7,7,3,2,5,3,11,8,9,4,3,6,4,5,10,5,7,4,6,3,5,6,4,4,1,3,14,6,6,3,2,1,6,7,7,2,4,10,5,6,6,8,5,12,1,4,10,5,7,3,7,3,21,10,8,5,3,6,5,13,3,11,3,5,15,19,5,9,2,3,8,4,7,7,5,5,5,4,4,3,4,7,7,3,8,14,5,7,9,9,3,10,6,8,10,1,2,10,5,8,9,3,2,9,7,4,7,5,7,9,11,2,6,3,10,4,6,7,3,4,6,5,9,15,9,2,10,7,4,15,3,4,4,4,6,2,5,4,10,7,4,5,3,12,9,2,5,9,6,7,5,7,3,20,9,9,13,9,3,13,8,6,3,7,15,7,6,8,5,2,9,4,4,8,13,9,13,4,5,5,6,8,2,8,9,5,9,1,16,7,6,6,8,4,6,7,8,7,10,13,9,3,5,6,2,5,8,7,5,2,7,7,2,11,2,3,1,4,7,7,8,3,4,5,7,1,4,13,6,10,8,11,5,11,4,2,3,9,7,12,7,3,12,8,10,7,2,10,10,9,5,9,7,5,9,5,3,3,2,6,5,16,6,1,4,6,15,5,2,3,2,1,5,4,9,3,3,7,9,3,4,9,5,20,4,4,15,5,10,6,5,5,6,4,1,4,5,8,8,7,4,2,4,1,4,12,22,5,11,1,8,12,7,10,1,2,4,11,3,6,10,2,4,5,5,18,7,9,8,4,11,2,10,5,6,6,3,5,20,7,3,6,5,2,3,9,5,11,9,14,1,17,8,2,4,15,10,5,13,4,8,4,10,7,9,18,9,4,2,13,10,12,5,5,4,5,6,8,5,7,4,6,7,6,4,8,9,9,4,10,4,9,10,3,4,11,6,8,2,2,4,2,9,14,3,12,9,7,4,8,4,11,10,3,7,4,5,3,6,9,6,5,9,3,4,7,11,5,6,5,6,3,9,1,9,5,5,7,6,8,8,7,5,3,21,10,2,7,6,10,1,7,8,7,2,9,4,6,11,10,12,7,9,11,10,10,2,6,9,3,4,3,9,8,5,10,3,4,5,12,7,5,1,6,5,4,4,10,2,5,8,8,9,5,4,6,4,7,6,7,12,1,8,12,5,1,5,20,2,13,3,5,4,5,6,18,9,4,17,8,12,6,5,6,3,10,11,6,5,4,4,6,4,8,8,4,4,8,3,13,7,11,4,4,5,3,6,7,6,14,3,5,10,9,8,6,6,18,3,6,7,11,3,8,6,6,2,6,4,4,7,3,8,12,2,9,4,3,3,3,6,3,8,17,3,9,5,6,1,6,5,3,1,1,5,7,3,2,4,6,12,3,8,7,11,2,5,9,11,6,2,3,3,3,7,3,7,6,16,13,7,5,8,8,2,3,9,5,4,5,4,2,3,4,6,5,21,2,15,4,3,8,4,5,6,2,4,7,6,3,8,8,6,6,7,2,5,8,4,2,4,5,11,14,3,9,1,4,4,5,15,6,13,9,8,5,6,3,4,9,2,1,4,7,10,1,10,2,11,6,2,6,4,4,7,3,1,3,12,3,4,10,10,6,3,2,3,1,8,13,7,4,8,9,1,3,7,12,6,5,8,5,4,6,11,11,7,8,6,2,6,9,1,9,4,10,1,7,4,3,17,1,6,9,4,7,5,3,7,2,1,4,10,11,5,7,9,9,3,8,3,2,12,6,7,7,19,9,4,16,3,4,6,6,9,2,7,6,2,5,6,9,9,7,4,4,8,4,10,2,9,7,14,7,5,5,5,7,5,12,6,9,4,3,8,7,10,15,8,4,1,7,8,8,7,4,12,1,9,8,4,8,4,6,3,12,11,11,4,5,6,5,6,6,1,5,3,1,6,4,4,10,11,4,6,3,6,8,4,8,2,1,10,6,9,5,4,10,2,6,10,1,8,8,10,10,11,2,4,5,9,1,1,1,8,8,10,3,9,5,7,13,12,8,2,6,3,9,6,3,5,5,11,4,15,2,9,4,5,6,8,5,17,2,11,3,2,4,4,4,6,1,11,6,7,12,2,5,4,10,9,2,3,7,3,7,5,4,6,9,8,6,2,7,4,2,3,8,9,7,4,7,7,2,7,2,7,3,4,6,7,4,4,15,10,2,5,5,4,1,2,9,12,10,6,5,12,1,3,5,10,7,5,21,4,2,10,7,7,3,12,4,3,1,7,4,5,3,5,4,2,4,11,2,3,2,1,8,3,5,7,8,4,3,1,4,5,7,3,1,6,4,8,2,12,3,6,22,6,2,3,3,2,3,5,7,5,7,3,5,8,2,10,4,3,13,3,5,5,4,5,1,7,8,7,3,7,5,4,4,8,3,8,2,6,6,4,3,6,5,3,3,5,2,6,6,10,3,8,1,7,3,4,5,4,10,4,2,1,3,6,5,15,10,10,2,4,15,1,5,7,3,2,11,4,7,9,4,7,7,2,4,5,28,5,5,9,7,10,4,10,4,2,7,13,9,4,3,11,7,1,8,3,9,14,4,5,12,6,7,5,5,3,5,5,5,8,3,9,1,3,19,8,3,3,5,5,5,5,11,2,20,1,7,8,4,5,3,2,7,4,2,7,8,11,7,8,13,10,3,4,7,10,2,10,7,6,13,9,7,3,6,1,8,6,6,4,12,9,5,9,4,9,3,20,7,2,8,10,7,6,4,11,3,4,9,6,10,11,1,2,4,8,6,4,14,3,4,6,6,2,5,7,7,6,10,11,19,12,6,7,8,4,11,11,18,5,6,6,15,5,3,9,12,7,7,11,9,23,8,7,3,11,11,2,3,5,7,1,3,4,10,7,2,10,4,10,9,8,7,5,4,4,4,3,7,7,6,7,4,6,3,4,8,5,4,3,6,7,2,8,3,2,10,6,3,6,3,9,11,9,8,9,2,13,9,12,11,10,13,4,11,11,1,1,3,1,4,6,5,6,3,13,3,3,3,3,3,6,7,6,7,7,10,9,5,6,5,3,12,3,2,5,7,3,3,4,4,3,10,14,11,4,4,4,9,5,8,4,1,12,5,4,8,2,6,4,9,4,8,4,4,8,2,7,7,4,3,4,5,5,6,15,6,12,5,1,7,9,5,5,10,8,2,3,3,7,8,6,9,8,3,12,1,3,3,5,3,4,2,4,5,3,9,3,5,8,7,14,4,7,8,3,6,7,4,4,5,4,3,6,7,2,5,10,7,3,10,2,4,6,4,9,3,5,6,10,6,8,6,10,5,2,6,4,6,9,3,6,2,4,5,3,4,11,14,1,8,5,2,6,2,4,9,3,2,4,11,7,11,4,7,3,2,12,5,7,5,8,2,2,8,8,3,4,5,7,10,5,5,9,3,5,6,6,1,15,9,9,3,7,3,9,15,1,5,3,4,3,5,6,5,9,4,4,6,10,9,8,6,1,2,3,5,6,3,4,5,3,9,4,3,6,6,6,6,15,10,9,3,4,10,8,5,4,4,4,7,4,5,2,4,14,2,6,8,7,5,11,2,5,3,8,12,3,4,17,6,4,10,6,4,5,4,3,7,8,5,1,2,1,5,4,4,4,4,4,6,9,11,5,5,3,6,2,1,3,1,10,2,4,3,6,12,3,5,12,5,1,4,9,8,5,5,5,7,2,4,6,13,3,3,4,3,2,7,6,5,6,5,2,5,2,8,16,11,5,4,3,3,6,4,7,10,3,4,6,4,1,4,3,2,2,2,2,11,9,9,5,3,4,4,6,4,2,8,9,7,5,5,13,3,10,4,5,3,3,3,2,6,5,8,4,5,1,10,5,2,3,2,7,7,6,1,4,2,7,7,7,7,3,9,3,6,10,4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5,1,4,2,3,3,1,2,2,3,2,10,3,8,4,4,1,1,6,3,2,1,4,9,13,3,3,1,4,6,3,2,8,4,1,3,2,13,6,3,1,6,2,8,3,11,8,1,2,6,2,11,3,1,4,1,1,1,4,4,1,4,11,2,2,7,1,5,3,3,2,2,6,1,1,1,2,2,4,1,3,3,1,3,3,3,2,1,5,11,3,1,3,3,2,5,3,1,4,3,7,3,2,4,1,4,2,2,1,8,4,4,6,2,9,3,6,3,1,2,3,2,1,2,2,2,2,6,3,2,3,1,2,5,5,1,3,1,1,6,2,2,1,7,1,4,10,5,2,10,1,1,1,2,2,3,4,1,4,2,6,4,2,4,2,1,1,2,5,1,1,3,2,2,2,1,3,2,1,4,4,5,2,1,9,1,3,3,2,7,5,1,3,4,12,1,3,5,3,9,2,2,1,3,6,1,1,4,3,2,1,3,4,2,2,2,1,2,1,1,5,2,2,1,4,9,2,6,5,1,1,3,1,9,1,7,8,3,7,4,5,5,5,11,3,1,3,1,8,4,7,5,2,3,11,2,1,7,1,4,2,4,1,1,4,3,3,3,2,9,1,4,6,5,2,11,1,2,3,1,1,4,7,4,3,4,4,4,5,1,1,2,8,2,2,5,1,3,1,3,3,5,10,3,4,7,2,2,2,4,3,4,4,2,5,1,3,1,5,5,2,1,2,2,1,4,17,2,1,5,3,4,1,2,6,2,6,11,3,11,2,1,2,11,9,2,1,3,1,3,4,2,1,3,1,3,1,1,2,3,7,5,5,2,2,2,3,1,3,2,3,1,2,5,3,6,3,1,5,1,1,6,4,1,1,1,5,2,3,8,1,3,1,5,5,1,4,4,3,1,3,4,3,6,5,18,1,1,2,3,3,1,2,1,3,6,2,5,1,2,5,3,3,5,2,2,5,3,2,4,10,3,5,3,6,7,2,3,5,1,1,1,1,2,1,3,6,3,1,6,1,8,2,6,3,2,4,1,4,2,1,2,3,9,5,1,1,6,1,4,2,1,5,2,1,3,1,6,7,5,1,1,5,4,1,1,4,1,7,2,1,1,8,2,1,1,3,4,1,3,1,3,1,3,3,8,1,2,2,1,8,1,2,8,5,1,2,2,3,1,2,2,4,5,1,1,2,3,1,1,4,2,4,1,3,2,1,3,1,4,12,14,1,5,3,2,4,5,1,5,3,2,1,3,1,1,2,5,1,1,2,7,2,4,4,2,1,6,12,1,5,6,1,1,2,2,1,9,9,1,2,3,4,1,7,2,12,2,2,3,3,2,2,6,1,2,3,3,3,3,1,4,8,2,2,6,5,3,4,2,3,1,2,4,1,7,6,8,2,3,4,2,5,1,5,1,2,1,4,3,4,2,2,3,9,6,4,1,3,1,3,2,3,2,2,3,3,2,1,2,1,1,3,2,3,1,1,8,4,5,2,4,2,4,2,1,3,7,1,1,3,1,2,2,2,1,2,2,1,1,1,7,2,2,1,1,4,2,2,5,1,2,1,3,1,4,3,1,5,5,4,3,1,1,4,3,3,1,1,1,2,1,7,5,3,1,1,4,2,4,5,2,1,2,4,3,2,3,3,6,4,4,5,2,5,1,4,6,3,2,6,3,4,5,3,3,1,2,1,9,2,4,6,5,3,2,4,5,4,1,3,3,6,2,2,2,4,2,10,3,2,9,1,3,1,4,2,5,2,7,2,7,1,1,2,4,3,2,1,3,4,3,6,1,1,5,2,2,1,2,6,2,2,1,2,1,4,5,3,1,2,1,1,3,3,3,5,3,4,1,1,1,3,1,2,2,2,42,4,1,6,1,1,6,1,3,2,4,1,2,2,1,4,1,3,3,2,5,1,6,1,2,3,4,1,3,1,4,5,2,9,2,1,3,7,2,15,1,1,1,2,7,4,1,3,1,3,2,5,3,2,2,1,5,6,3,2,9,1,1,8,1,1,1,1,2,2,2,2,2,9,3,4,2,2,1,4,3,2,4,2,5,2,1,2,4,1,3,2,1,2,2,1,3,2,3,1,2,2,2,1,5,2,1,7,1,5,1,1,1,3,3,1,2,13,2,3,4,1,2,2,1,5,2,3,2,2,1,1,1,2,5,3,5,1,1,2,5,2,7,1,5,2,5,3,4,2,1,1,6,3,5,3,2,1,4,1,2,1,7,1,1,1,3,1,1,1,1,1,7,1,2,1,3,2,3,1,1,6,3,1,4,5,1,3,2,1,2,2,7,2,6,2,2,3,3,2,6,2,3,7,5,2,5,1,1,1,3,2,1,2,1,2,1,3,3,1,2,3,2,1,1,3,1,2,2,6,2,6,2,1,3,1,1,1,2,3,3,11,5,1,1,2,6,1,2,2,1,1,1,2,2,2,1,3,2,5,2,1,4,5,4,1,2,1,1,1,3,2,1,9,1,1,2,6,2,2,1,1,1,1,1,3,1,4,2,1,2,2,1,4,1,1,2,1,2,2,2,6,1,5,5,1,1,2,2,5,2,5,1,1,2,1,2,2,2,4,2,3,1,1,3,3,4,3,2,3,2,1,1,1,2,3,2,1,3,3,2,2,1,2,5,2,1,3,3,1,1,2,1,2,1,5,1,1,1,1,1,1,1,1,7,4,1,3,1,1,1,1,2,1,1,5,5,2,2,2,1,3,1,12,1,1,3,1,2,3,1,1,3,1,3,1,1,1,1,1,3,1,2,1,4,1,8,2,1,1,2,1,1,1,2,1,1,2,1,1,1,2,3,3,1,2,1,1,3,2,5,3,2,6,1,2,2,1,3,2,1,2,5,5,3,2,2,2,5,2,5,7,1,2,1,2,5,1,5,1,2,1,3,3,4,2,1,1,5,3,1,2,2,2,1,7,2,4,1,2,1,2,1,1,3,2,2,6,3,2,3,8,1,3,1,1,2,2,2,1,5,5,1,1,3,3,5,1,1,1,1,3,2,1,1,10,1,1,1,1,1,2,3,3,1,3,2,2,4,4,1,1,3,2,3,4,1,1,9,3,1,2,4,1,6,1,1,3,3,1,2,2,1,1,1,1,1,2,4,2,1,1,1,4,1,3,1,1,1,2,1,2,1,1,4,1,2,2,3,2,1,1,2,5,1,1,1,2,4,5,2,2,2,2,9,3,3,2,2,3,5,2,2,1,1,1,2,2,1,1,1,3,4,2,1,1,3,3,1,4,3,5,2,4,2,10,1,1,3,2,1,1,1,1,1,5,1,1,2,3,1,2,4,2,2,1,4,1,1,3,1,1,3,1,1,4,5,1,1,2,1,3,1,1,3,2,1,1,1,3,1,4,1,1,3,4,1,1,2,1,2,1,4,3,2,1,6,1,4,1,1,1,5,1,2,3,3,3,2,1,6,4,2,1,1,4,1,1,2,1,1,2,2,2,3,1,1,2,1,2,1,6,1,3,6,1,1,1,4,2,1,1,1,1,6,1,1,3,1,1,1,1,2,1,1,1,2,2,1,1,6,2,1,1,2,1,2,1,1,1,1,1,1,2,1,1,1,6,4,1,2,2,2,3,1,1,1,1,2,10,1,3,1,2,2,3,1,1,1,1,1,3,4,2,12,1,1,3,5,1,1,1,1,1,2,2,1,2,1,1,1,1,1,1,5,1,3,4,2,2,5,1,2,1,2,1,1,1,1,3,1,1,4,1,1,1,1,1,2,2,1,3,1,2,1,2,2,2,2,2,1,1,2,2,1,1,1,1,1,2,1,1,1,3,1,1,1,3,1,1,1,4,1,4,1,1,2,6,1,4,1,2,2,1,1,1,4,1,6,1,1,1,3,2,1,1,3,1,1,1,2,2,2,2,1,2,2,3,5,1,7,2,1,3,3,1,1,3,3,2,1,1,2,1,1,1,4,1,2,1,1,2,1,3,2,2,5,1,1,1,2,1,2,1,1,1,1,1,1,10,2,4,1,2,2,1,1,1,1,1,6,1,1,2,2,6,1,1,1,7,1,1,1,1,1,3,1,1,1,1,2,1,1,2,1,1,3,2,1,1,1,2,1,2,1,1,3,1,1,1,1,1,2,1,3,1,1,1,1,1,3,4,1,1,4,4,1,1,2,2,8,1,2,2,3,1,1,1,4,3,1,1,2,1,1,1,1,1,2,1,2,2,1,1,3,1,1,2,1,1,3,2,3,1,1,1,1,1,1,1,1,1,1,2,4,1,3,1,1,10,2,1,1,1,1,1,2,4,1,5,1,3,2,1,1,1,1,1,1,1,1,1,1,4,1,2,1,2,1,1,1,2,1,1,1,1,1,5,2,1,2,3,1,1,1,4,2,1,2,1,1,1,1,2,1,1,2,2,2,4,3,1,3,1,7,1,4,1,1,3,2,1,3,4,4,1,4,1,2,3,1,1,1,1,1,1,1,3,3,1,1,1,2,1,2,1,1,1,1,1,1,1,1,1,2,4,1,5,1,1,2,1,2,1,1,1,1,1,1,2,2,1,1,2,1,5,6,1,1,1,4,2,1,1,2,3,3,1,1,2,1,1,2,1,1,1,2,1,1,3,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,3,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,2,1,1,1,2,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,3,1,1,1,1,3,1,1,1,2,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,1,7,1,1,1,3,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,3,3,1,1,1,2,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1)
rf_count_x=c(0,1,2)
rf_count_y=c(0,1,2)

        pdf("/data/mus/lg/projects/de_novo_assembly/summary/MK_02_TTAGGC_TTAGGC_L008_RX_001.hist.pdf", paper="a4r")

        par(omi = c(0,0,0,0), mar=c(0,0,0,0), mai=c(0,1,0,0), oma = c(0,0,0,0))
        #par(omi = c(0,0,0,0), mar=c(0,0,0,0))
        #par(mfrow=c(2,1), mai=c(0,1,0,0), oma = c(0,0,0,0))
        layout(matrix(c(1,2), 2, 1, byrow = TRUE), heights = c(2,3),widths = c(1,1))

        do_plot <- function(rf_count_x_orig, rf_count_y_orig, fr_count_x_orig, fr_count_y_orig, xranges, bin_size)
        {
          rf_count_x = round(rf_count_x_orig / bin_size + bin_size / 2)
          rf_count_y = aggregate(rf_count_y_orig, list(rf_count_x), FUN = sum)$x
          rf_count_x = aggregate(rf_count_x_orig, list(rf_count_x), FUN = mean)$x
          fr_count_x = round(fr_count_x_orig / bin_size + bin_size / 2)
          fr_count_y = aggregate(fr_count_y_orig, list(fr_count_x), FUN = sum)$x
          fr_count_x = aggregate(fr_count_x_orig, list(fr_count_x), FUN = mean)$x

          rf_count_y <- subset(rf_count_y, rf_count_x >= xranges[1] & rf_count_x <= xranges[2])
          rf_count_x <- subset(rf_count_x, rf_count_x >= xranges[1] & rf_count_x <= xranges[2])
          fr_count_y <- subset(fr_count_y, fr_count_x >= xranges[1] & fr_count_x <= xranges[2])
          fr_count_x <- subset(fr_count_x, fr_count_x >= xranges[1] & fr_count_x <= xranges[2])

          plot  (fr_count_x, fr_count_y, type='l', xlim = xranges, xlab = "",
        	 ylab = "Counts",   col = 'black', omi = c(0,0,0,0), xaxt = 'n')
          points(rf_count_x, rf_count_y, type='l', col = 'blue')

          legend(x = "topleft", fill=c("black", "blue"), bty = "n", border = NULL, legend = c('FR', "RF"))


          par(mai=c(1,1,0,0))
          fr_count_y = cumsum(fr_count_y)
          rf_count_y = cumsum(rf_count_y)
          plot  (fr_count_x, fr_count_y, type='l', xlim = xranges,
        	 xlab = "Insert sizes", ylab = "Cummulative counts", mar =c(0,0,0,0),
        	 col = 'black')
          points(rf_count_x, rf_count_y, type='l', col = 'blue')
          legend(x = "topleft", fill=c("black", "blue"), bty = "n", border = NULL, legend = c('FR', "RF"))

          median_index = min(which(fr_count_y > max(fr_count_y) / 2))
          points(c(0, fr_count_x[median_index], fr_count_x[median_index]),
              c(fr_count_y[median_index], fr_count_y[median_index], 0), col = 'red', type='l')

          text(xranges[1], fr_count_y[median_index]*1.5, pos = 4,
              labels = paste("median = ", fr_count_x[median_index], "
bp count = ", max(fr_count_y), " pairs between [", xranges[1], " & ", xranges[2], "]"))
        }

        do_plot(rf_count_x, rf_count_y, fr_count_x, fr_count_y, c(20000,50000), 200)
        do_plot(rf_count_x, rf_count_y, fr_count_x, fr_count_y, c(0,1000)     , 1)
        do_plot(rf_count_x, rf_count_y, fr_count_x, fr_count_y, c(0,70000)    , 200)

                              dev.off()
        
null device 
          1 
